Purchasing Negative EV a Good Deal in Terms of the Lottery?

[Roland32]

Over the years in the STT Forum there has been a lot of discussion about whether or not you should pass on +ev situations if you belief it will keep you from taking advantage of an even higher opportunity later. Coupled with taking -ev situations if you belief it is the least ev spot you are likely to find. This made me wonder about the lottery.

I have always heard that the lottery is a bad bet because it is highly -ev. But the cost per unit is really low and irrelevant until it cumalates. This is especially true when related to the amount of the jackpot, however remote.

Now based upon the basic principle that it is easier for a Billionaire to make another million compared to a millionaire, which in turn is also exponentially greater than of a thousandaire or hundredaire.

Because this is the case is it that the later ability to more easily gain addtional monies offset the initial negative investment of the lottery? What would the proportions have to be? Are there any poker situations where the money would be deep enough for this to oocur as well? (This last one I remember debating a while ago but dont remember if there was any consensus or not.)

[soon2bepro]

But often the unit is relevant enough to matter when you add it up. The idea that you will only make this -EV bet once is flawed, because with that philosophy you will keep taking -EV bets at everything, and say to yourself "it's only once".

The only scenario that I can think of where playing the lottery is +EV is when the unit(s) you're betting are truly irrelevant to you, and in fact your whole chance of happiness or financial success depends upon winning the lottery. Say you're homeless and have nothing but one buck in your pocket. If there's no way you can steal/make more money, you're going to die within a few days, or at least be very unhappy and without chance of improvement. In this case you can just play the lottery and see if you're lucky enough. Because you truly have nothing to lose. But if you're making $1500 a week, it may look like $1 is irrelevant, but it's not when compared to the ridiculously low chance of winning the lottery. In other words, if it's ok to bet $1 a week for the lottery in this situation, it'd be ok to bet $20. And to bet $500, etc, etc... But it's not.

A similar, more common example to the homeless guy playing the lottery would be a well established person paying insurance policy for something. It's -EV, but in some cases it's ok to sacrifice EV if that saves you from disaster, or gives you the best chance to end up better, averagely.

A common poker situation of this is when good players go above their bankroll limitations and think "if i can just get a good swing, i'll be on my track to making much more money"... But what they don't realize is that they're just as likely to have a similar sized bad swing, and in this case they'll be on their way to making much less money, or none at all. If they had stayed within their bankroll limitations they would've went up slowly but steady.

I know a lot of very good players who lost their bankrolls time and again like this, having to start over grinding it at 0.5/1 NL or so...

[Roland32]

In regards to your post also considered is the proportional relationship to the possible gained benefit of winning. What that proportion is however i dont know. I mean would interest alone over say 20 years at 10% offset the intitial loss? What would be the formula to that? something like:
Cost per try(e.v.)+ (additional monies made because of jackpot) = (Jackpot)
Im sure a math person could figure out a formula. The main point is that it is much easier to make money when you have alot of it. What the proportion is, I don't know. But There is a point at which if the additional benefits were great enough it would offset the -ev of the initial investment.

I think the cumalative effect is important and is tied into the proportion of the most desired result. I think there is a world of difference between $1 bet and a $200 bet and 200 $1 bets over 2+ years and 1 $200 bet.
The other side has to do with the initial investment itself. If one can "afford" the loss and the benefit would give rise to additional benefits thaat are not monetary added it would make it possibly a +ev situation. But if the cost reaches a certain point per try the additional benefits would no longer apply, even though the proportion would be the same. I intuitively feel this is correct but I cant prove it, or dont know how.

Edit: After thinking I think it would be because as the cost per try goes up additional negative costs are now added in. I.E. cant afford to take woman out becuase you spent your cash on the lotto would now proportionally offset the additional benefits gained outside of the jackpot itself.